Do you need a sphere that is covered completely in hexagons of equal size? That isn't possible, but a sphere covered by all hexagons except for twelve pentagons is pretty straightfoward to contruct. Starting with a icosohedron, subdivide each face to the appropriate resolution, project onto a sphere, and create the hexagons by connecting midpoints of the resulting triangles. The corner tiles of the original icosohedron are pentagons, but the rest of the sphere will be covered by hexagons.
The technical term for this structure is a geodesic polyhedron, with faces grouped into hexagons and pentagons.
It is not perfect if you want only hexagons on a sphere, but for many applications it is probably good enough.
This is a javascript implementation of the above method. I use it to build the Encom Globe, and it could be used for games or other "useful" applications. At the very least this might be useful as a reference implementation for people trying to something similar.
The basic usage is as follows:
var radius = 15; // Radius used to calculate position of tiles
var subDivisions = 5; // Divide each edge of the icosohedron into this many segments
var tileWidth = 0.9; // Add padding (1.0 = no padding; 0.1 = mostly padding)
var hexasphere = new Hexasphere(radius, subDivisions, tileWidth);
for(var i = 0; i< hexasphere.tiles.length; i++){
// hexasphere.tiles[i].centerPoint contains x,y,z of the tile
// hexasphere.tiles[i].boundary contains an ordered array of the boundary points
// hexasphere.tiles[i].neighbors contains a list of all the neighboring tiles
}
var waveformObjString = hexasphere.toObj() // export as waveform .obj to use in 3d modelling software
var jsonString = hexasphere.toJson() // export it as a json objectCheck out a demo on my website. The demo uses Three.js to render the sphere, but that is not an inherit dependency of hexasphere.js. You can generate a waveform (.obj) model directly from the website, if you don't want to deal with the javascript library.
If you port this to other languages, let me know and I'll link to it here:
- Objective-C: pkclsoft/HexasphereDemo
- Unity C#: Em3rgencyLT/Hexasphere
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